How to grid-fill a spiral
There is an addon called F2 (comes bundled with Blender by default) which could speed this up.

To enable the addon go to File > User Preferences > Addons (or Ctrl+Alt+U) and search for F2 and enable it.



Once enabled, this addon adds two new functions to the F key, one of which should speed up your workflow considerably (the other is described here).  Just create the first face of the spiral, then select the inside edge of the new face and hit F to create a new face along the spiral.  Then keep pressing F until you have filled the spiral.